Alumina ceramic material - Mat110 : should it be coupled with EOS ?

[GearDyn 1]

Hello all, 

i'm modelling a ballistic impact on Alumina ceramic targets , & will be utilising  Mat 110  ( reference journal  as shown below).... 

Query is , should we use EOS while using this material? if so , which EOS is better 

Also if the unit consistency is changed , where to get the conversion factors for the parameters ? 

  mm s

Reference Journal : Steel spheres impact on alumina ceramic tiles: Experiments and finite element simulations : Genevieve Toussaint

(https://www.researchgate.net/publication/333938585_Steel_spheres_impact_on_alumina_ceramic_tiles_Experiments_and_finite_element_simulations)

thanks in advance

[James Kennedy]

Dear GearDyn,

 

In LS-DYNA, MAT_110 (also known as MAT_STEINBERG_HY) is a material model designed for simulating elastic-plastic, hydrodynamic materials under extreme conditions, such as high strain rates and shock waves. It requires a separate equation of state (EOS) to define the pressure-volume-internal energy relationship of the material. The coupling of MAT_110 with an EOS is what allows for accurate modeling of these high-pressure, high-strain-rate phenomena. 

 

The role of an EOS with MAT_110 

 

MAT_110 calculates the material's deviatoric stress, which is its strength behavior.

 

The separate EOS calculates the hydrostatic (or bulk) pressure, which is the volume-dependent part of the stress.

 

The total stress is the sum of the deviatoric stress from MAT_110 and the pressure from the selected EOS. 

 

Common equations of state used with MAT_110 

 

While any compatible EOS keyword can be used, the Gruneisen EOS is the most common choice for modeling solids with MAT_110 under shock compression. Other options include: 

 

EOS_GRUNEISEN: A popular choice for modeling the hydrodynamic behavior of metals and other solids under shock loading.

 

EOS_LINEAR_POLYNOMIAL: A more general-purpose EOS that can be used for a wide range of materials. For low to moderate strain rates, it can approximate the material's bulk modulus.

 

EOS_TABULATED: This option allows you to define the pressure-volume relationship via a user-defined table, offering maximum flexibility. 

 

Input for an EOS in LS-DYNA 

 

The specific input parameters depend on the chosen EOS. For example, to define the Gruneisen EOS, you would use the *EOS_GRUNEISEN keyword with parameters like: 

 

Reference density (𝜌0)

 

Sound speed in the material (𝐶)

 

Dimensionless material coefficients (S1,S2,S3)

 

Gruneisen gamma (𝛾0)

 

Correction term (𝑎)

 

This information is typically defined on a separate card following the *MAT_110 material properties. 

 

When to use an EOS with MAT_110 

 

The use of an EOS is essential when simulating phenomena involving: 

 

High-velocity impacts: A projectile impacting a target at high speed.

 

Shock wave propagation: Explosions or other events that cause high-pressure shock waves.

 

High strain rates: Deformations at rates exceeding 10^5 per second.

 

Pressure-dependent material behavior: Materials where the bulk pressure significantly affects the yield strength. 

 

Sincerely,

James M. Kennedy

KBS2 Inc.

August 27, 2025

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[James Kennedy]

Hello all, 

--

[James Kennedy]

Dear GearDyn,

 

Some links you might study for unit conversion

 

https://www.dynasupport.com/howtos/general/consistent-units

 

unit conversion ls dyna calculator

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[GearDyn 1]

Thanks James for the insights ,

but when i'm trying to include EOS , im getting the error which says Mat110 does not need EOS. 

But when the EOS is removed , the calc run perfectly

Thanks in advance, Harsha

[James Kennedy]

Dear GearDyn,

 

My apologies, my search engine failed me. MAT_110  and MAT_010 appear to have got mixed somehow.  

 

Notes from the following link indicates that no EOS is requireD for MAT_110

 

https://lsdyna.ansys.com/dynamat/#:~:text=This%20is%20Material%20Type%2010,of%20state%20determines%20the%20pressure.

 

MAT_­011

*MAT_­STEINBERG

HY, MT

FAIL, EOS, TEF, TC

This is Material Type 11. This material is available for modeling materials deforming at very high strain rates (> 10^5 per second) and can be used with solid elements. The yield strength is a function of temperature and pressure. An equation of state determines the pressure. This model is applicable to a wide range of materials, including thos with pressure-dependent yield behavior. In addition, the incorporation of an equation of state permits accurate modeling of a variety of different materials. The spall model options permit incorporation of material failure, fracture, and disintegration effects under tensile loads.

 

*MAT_­110

*MAT_­JOHNSON_­HOLMQUIST_­CERAMICS

CR, GL

SRE, FAIL, DAM, TC

This is Material Type 110. This Johnson-Holmquist Plasticity Damage Model is useful for modeling ceramics, glass and other brittle materials. A more detailed description can be found in a paper by Johnson and Holmquist [1993].

 

JH-2 primary references:

 

Johnson, G.R., and Holmquist, T.J., "An Improved Computational Constitutive Model for Brittle Materials", High-Pressure Science and Technology - 1993, American Institute of Physics, Vol. 309, pp. 981-984, July, 1994.

 

Johnson, G.R., and Holmquist, T.J., "Response of Boron Carbide Subjected to Large Strains, High Strain Rates, and High Pressures", Journal of Applied Physics, Vol. 85, No. 12, pp. 8060-8073, June, 1999.

 

Sincerely,

James M. Kennedy

KBS2 Inc.

August 29, 2025